Assuming movable block entities are enabled, double chests will move when pushed or pulled directly, but they don't stick to sticky blocks like slime or honey.

Example setups:

Observed behavior:

• The left sticky piston pushes and pulls the entire double chest.
• The middle sticky piston pushes and pulls the slime block, and the chest next to it is dragged along.
• The right sticky piston pushes and pulls the slime block, but the double chest does not move along with it.

Expected behavior:

• When the right sticky piston moves the slime block, the double chest should move along with it, like the single chest does. The left sticky piston demonstrates that double chests do not seem to be "non-sticking" blocks like glazed terracotta, as the double chest can be pulled by the retracting piston, so not sticking to slime (or honey) is inconsistent behavior.

Tested with Zeta 1.0-14 and Quark 4.0-439.